Consider a chess board. Let the total number of possible rectangles and squares be and respectively.
If the limit above is in the form of for coprime positive integers , find .
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R n = ( n + 1 2 ) ( n + 1 2 ) = 4 n 2 ( n + 1 ) 2 S n = 1 ∑ n r 2 = 6 n ( n + 1 ) ( 2 n + 1 ) L = n → ∞ lim 2 ( 2 n + 1 ) 3 ( n + 1 ) = n → ∞ lim 2 ( 2 + n 1 ) 3 ( 1 + n 1 ) = 4 3
Here For calculating Rectangles There are n+1 Horizontal lines and n+1 vertical Lines so we select any two Vertical and any two horizontal Lines So that Rectangle is formed (and obviously squares are also rectangles)
You may Take Eg as Our Planet Chess Board ,(8*8) in This 9 are vertical and 9 horizontal lines are present.
Karan Keep it up bro ! Keep Posting such more :)